delta-bar-delta and directed random search algorithms application to reduce transformer switching...

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International Journal on Electrical Engineering and Informatics - Volume 5, Number 1, March 2013

Delta-Bar-Delta and Directed Random Search Algorithms Application to

Reduce Transformer Switching Overvoltages

Iman Sadeghkhani1, Abbas Ketabi2, and Rene Feuillet3

1Department of Electrical Engineering, Najafabad Branch, Islamic Azad University,

Najafabad 85141-43131, Iran2

Department of Electrical Engineering, University of Kashan, Kashan 87317-51167, Iran3Grenoble Electrical Engineering Lab (G2ELab), Grenoble INP, France

Abstract: This paper proposed an artificial neural network (ANN)-based approach to

mitigate harmonic overvoltages during transformer energization. Uncontrolled

energization of large power transformers may result in magnetizing inrush current ofhigh amplitude and switching overvoltages. The most effective method for the

limitation of the switching overvoltages is controlled switching since the magnitudes of

the produced transients are strongly dependent on the closing instants of the switch. Weintroduce a harmonic index that its minimum value is corresponding to the best case

switching time. Also, in this paper three learning algorithms, delta-bar-delta (DBD),

extended delta-bar-delta (EDBD) and directed random search (DRS) were used to train

ANNs to estimate the optimum switching instants for real time applications. ANNs

training is performed based on equivalent circuit parameters of the network. Thus,trained ANN is applicable to every studied system. To verify the effectiveness of the

proposed index and accuracy of the ANN-based approach, two case studies are

presented and demonstrated.

Keywords: Artificial neural networks, delta-bar-delta, directed random search

algorithm, harmonic index, switching overvoltages, transformer energization.

1. IntroductionA major process of power system restoration following a blackout would be energization of

primary restorative transmission lines in most countries [1-4]. The energizing process begins

by starting black-start generators such as hydro generators or gas turbines, and then charging

some pre-defined transmission lines to supply cranking power for large generation plants [5,6].Then the energization of unloaded transformers would be followed by switching action, and

that is an inevitable process of bottom-up restoration strategy. During transformer energization,unexpected over-voltage may happen due to nonlinear interaction between the unloaded

transformer and the transmission system [1,2]. When a lightly loaded transformer is energized,the initial magnetizing current is generally much larger than the steady-state magnetizing

current and often much larger than the rated current of the transformer [7-8]. Controlled

switching has been recommended as a reliable method to reduce switching overvoltage during

energization of capacitor banks, transformers, and transmission lines [9]. This technique is the

most effective method for the limitation of the switching transients since the magnitudes of thecreated transients are strongly dependent on the closing instants of the switch [10].

The fundamental requirement for all controlled switching applications is the precise

definition of the optimum switching instants [10]. This paper presents a novel method forcontrolled energization of transformers in order to minimize temporary overvoltages. We

introduce a harmonic index to determine the best case switching time. Using numerical

algorithm we can find the time that the harmonic index is minimum, i.e., harmonicovervoltages is minimum. Also, for real time applications, this paper presents an Artificial

Received: May 3rd, 2012. Accepted: March 8th, 2013

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Neural Network (ANN)-based approach to estimate optimum switching angle during

transformer energization. Three learning algorithms, delta-bar-delta (DBD), extended delta-bar-delta (EDBD) and directed random search (DRS) were used to train ANNs. The proposed

ANN is expected to learn many scenarios of operation to give the optimum switching angle in

a shortest computational time which is the requirement during online operation of powersystems. In the proposed ANN we have considered the most important aspects, which

influence the inrush currents such as voltage at transformer bus before switching, equivalent

resistance, equivalent inductance, equivalent capacitance, line length, line capacitance,

switching angle, and remanent flux. This information will help the operator to select the properbest-case switching condition of transformer to be energized safely with transients appearing

safe within the limits.

2. Harmonic Overvoltages Study during Transformer EnergizationOne of the major concerns in power system restoration is the occurrence of overvoltages as

a result of switching procedures [2]. The major cause of harmonic resonance overvoltages

problems is the switching of lightly loaded transformers at the end of transmission lines. After

transformer energization, inrush currents with significant harmonic content up to frequencies

around ten times of system frequency are produced. The harmonic current components of the

same frequency as the system resonance frequencies are amplified in case of parallelresonance, thereby creating higher voltages at the transformer terminals [11]. This leads to a

higher level of saturation resulting in higher harmonic components of the inrush current which

again results in increased voltages. They may lead to long lasting overvoltages resulting inarrester failures and system faults and prolong system restoration [2]. This can happen

particularly in lightly damped systems, common at the beginning of a restoration procedure

when a path from a black-start source to a large power plant is being established and only a few

loads are restored yet [1,7,12].

The root cause of this phenomenon is the unfavorable combination of the sourceimpedance, the shunt capacitance of the energized circuits, the non-linear magnetizing

characteristics of the energized transformer, inadequate damping of the system and the source

voltage phase angle at the moment the transformer is energized. Key factors for the harmonic

overvoltages analysis can be listed as follows:

The resonance frequency of the network; The system damping including the network losses, and the load connected to the network; The voltage level at the end of the EHV lines; The saturation characteristic of the transformers; The remanent fluxes in the core of the transformer; The closing time of the circuit breaker pole;3. Study System Modeling

Simulations presented in this paper are performed using the PSB [13]. This program has

been compared with other popular simulation packages (EMTP and Pspice) in [14]. In [15]

generators have been modeled by generalized Parks model that both electrical and mechanicalpart are thoroughly modeled, but it has been shown that a simple static generator model

containing an ideal voltage source behind the sub-transient inductance in series with the

armature winding resistance can be as accurate as the Park model. Thus in this work,

generators are represented by the static generator model. Phases of voltage sources are

determined by the load flow results. Transmission lines are described by the distributed line

model. This model is accurate enough for frequency dependent parameters, because thepositive sequence resistance and inductance are fairly constant up to approximately 1 KHz [16]

which cover the frequency range of harmonic overvoltages phenomena. The transformer modeltakes into account the winding resistances (R1,R2), the leakage inductances (L1,L2) as well as

the magnetizing characteristics of the core, which is modeled by a resistance, Rm, simulating

the core active losses and a saturable inductance, Lsat. The saturation characteristic is specified

Iman Sadeghkhani, et al.

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Figure 2. Impedance at bus 2.

Figure 3. Changes of harmonic currents and Windex with respect to the switching angle.

Figure 4. Voltage at bus 2 after switching of transformer for best switching condition.

0 60 120 180 240 300 360 420 480 540 6000

0.5

1

1.5

2

2.5

3

Frequency [Hz]

ImpedanceZbus2

[p.u.]

0 10 20 30 40 50 60 70 80 900

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Switching Angle [deg.]

InrushCurrentHarmoni

cs[p.u.]

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.21.4

Time [s]

Voltage[p.u.]


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Table 1.Effect of Switching Angle on the Minimum of Overvoltages and Duration

of Vpeak> 1.3 p.u.

Switching Angle [deg.] Vpeak[p.u.] Duration of (Vpeak> 1.3 p.u.) [s]

56 1.1857 0

45 1.5104 0.3752

33 1.6527 0.4253

70 1.3892 0.1442

10 1.5861 0.3248

5. The Artificial Neural NetworkTe The basic structure of the Artificial Neural Network (ANN) is shown in Figure 5. The

ANN consists of three layers namely, the inputs layer, the hidden layer, and the output layer.

Training a network consists of adjusting weights of the network using a different learning

algorithm [17-20]. In this work, ANNs are trained with the two supervised and onereinforcement learning algorithms. In this paper, the delta-bar-delta (DBD), the extended delta-

bar-delta (EDBD) and the directed random search (DRS) were used to train the ANN [21]. To

improve the performance of ANNs, tangent hyperbolic activation function was used. Alearning algorithm gives the change wji(k) in the weight of a connection between neurons iandj. Error is calculated by the difference of PSB output and ANN output:

100PSB

PSBANNError(%) = (2)

In the next section, these learning algorithms have been explained briefly.

Figure 5.The structure of artificial neural network.

A.Delta-bar-delta (DBD) algorithmThe DBD algorithm is a heuristic approach to improve the convergence speed of theweights in ANNs [22]. The weights are updated by

)()()()1( kkkwkw +=+ (3)

Delta-Bar-Delta and Directed Random Search Algorithms Application

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where )(k is the learning coefficient and assigned to each connection, )(k is the gradient

component of the weight change. )(k is employed to implement the heuristic for

incrementing and decrementing the learning coefficients for each connection. The weighted

average )(k is formed as

)1()()1()( += kkk (4)

where is the convex weighting factor. The learning coefficient change is given as

=

otherwise0

0)()1()(

0)()1(

)( kkk

kk

k

(5)

where is the constant learning coefficient increment factor, and is the constant learning

coefficient decrement factor.

B.Extended delta-bar-delta (EDBD) algorithmThe EDBD algorithm is an extension of the DBD and based on decreasing the training time

for ANNs [23]. In this algorithm, the changes in weights are calculated from:

)()()()()1( kwkkkkw +=+ (6)

and the weights are then found as

)()()1( kwkwkw +=+ (7)

In Eq. (6), )(k and )(k are the learning and momentum coefficients, respectively. The

learning coefficient change is given as

=

otherwise0

0)()1(if)(

0)()1(if)(exp(

)( kkk

kkka

k

(8)

where is the constant learning coefficient scale factor, exp is the exponential function,

is the constant learning coefficient decrement factor, and is the constant learning

coefficient exponential factor. The momentum coefficient change is also written as

=

otherwise0

0)()1(if)(

0)()1(if)(exp(

)( kkk

kkk

k

(9)

where is the constant momentum coefficient scale factor, is the constant momentum

coefficient decrement factor, and is the constant momentum coefficient exponential factor.


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Figure 1. In this case, values of equivalent resistance, equivalent inductance and equivalentcapacitance are 0.00291 p.u., 0.02427, and 2.474 p.u., respectively. For testing trained ANN,

values of voltage at transformer bus (bus 19), line length, and remanent flux are varied and in

each step, optimum switching angle values are calculated from trained ANN and proposed

method. Table 2 contains the some sample result of test data of case 1.

Table 2. Case 1 some sample testing data and output

Delta-bar-delta algorithm:

V [p.u.]L.L.

[km]r [p.u.]

B.S.A.HI[deg.]

B.S.A.DBD[deg.]

Error [%]

0.9243 100 0.2 80.6 79.0 2.0150

0.9541 150 0.3 37.5 37.9 1.0054

1.0195 200 0.4 18.3 18.9 3.1244

1.0481 230 0.4 44.8 44.7 0.3241

1.0977 250 0.5 62.1 62.7 1.0237

1.0977 250 0.6 89.7 87.1 2.8766

1.1505 270 0.7 67.7 70.1 3.4791

1.1776 290 0.8 32.6 32.7 0.2374

Extended delta-bar-delta algorithm:

V [p.u.]L.L.

[km]r [p.u.]

B.S.A.HI[deg.]

B.S.A.EDBD[deg.]

Error [%]

0.9243 100 0.2 80.6 81.4 0.9450

0.9541 150 0.3 37.5 37.9 1.0209

1.0195 200 0.4 18.3 18.8 2.8778

1.0481 230 0.4 44.8 44.2 1.4402

1.0977 250 0.5 62.1 63.2 1.8443

1.0977 250 0.6 89.7 86.8 3.2207

1.1505 270 0.7 67.7 68.6 1.3270

1.1776 290 0.8 32.6 33.3 2.2361

Directed random search algorithm:

V [p.u.]L.L.

[km]r [p.u.]

B.S.A.HI[deg.]

B.S.A.DRS[deg.]

Error [%]

0.9243 100 0.2 80.6 78.3 2.8808

0.9541 150 0.3 37.5 36.8 1.8974

1.0195 200 0.4 18.3 18.2 0.3234

1.0481 230 0.4 44.8 45.3 1.0335

1.0977 250 0.5 62.1 60.8 2.1078

1.0977 250 0.6 89.7 89.1 0.6399

1.1505 270 0.7 67.7 66.0 2.5661

1.1776 290 0.8 32.6 33.2 1.9211


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Figure 6.Studied system for case 1.

V = voltage at transformer bus before switching, L.L. = line length, r = remanent flux,B.S.AHI = the best switching angle obtained by the harmonic index, B.S.ADBD = the best

switching angle obtained by the DBD, B.S.AEDBD= the best switching angle obtained by the

EDBD, B.S.ADRS= the best switching angle obtained by the DRS, and Error =switching angleerror.

B. Case 2As another example, the system in Figure 7 is examined. In the next step of the restoration,

unit at bus 6 must be restarted. In order to provide cranking power for this unit, the transformer

at bus 6 should be energized. In this condition, harmonic overvoltages can be produced because

the load of the transformer is small. After converting this system to equivalent circuit of Figure

1, various cases of transformer energization are taken into account and corresponding optimumswitching angles are computed from proposed method and trained ANN. In this case, values of

equivalent resistance, equivalent inductance and equivalent capacitance are 0.00577 p.u.,

0.02069, and 0.99 p.u., respectively. Summery of few result are presented in Table 3. It can beseen from the results that the ANNs are able to learn the pattern and give results to acceptable

accuracy.

Figure 7. Studied system for case 2.

Conclusion

This paper presents an ANN application to evaluate optimum switching condition during

transformer energization for real time application. The proposed method is based on theharmonic index which integrates the key parameters of overvoltages generation. The minimum

value of this index is corresponding to the best switching time for the transformer energization.

The delta-bar-delta, extended delta-bar-delta and directed random search has been adopted to

train ANN. Training ANN is based on equivalent circuit parameters to achieve goodgeneralization capability for trained ANN. Simulation results confirm the effectiveness and

accuracy of the proposed harmonic index and ANNs scheme.


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Table 3. Case 2 some sample testing data and output

Delta-bar-delta algorithm:

V [p.u.]L.L.

[km]r [p.u.]

B.S.A.HI[deg.]

B.S.A.DBD[deg.]

Error [%]

0.9335 125 0.8 75.4 74.6 1.0268

0.9512 155 0.7 42.9 42.8 0.2798

0.9906 175 0.6 56.1 54.3 3.2491

0.9906 175 0.5 90 89.5 0.5837

1.0502 215 0.4 82.3 83.4 1.3537

1.0595 225 0.3 29.4 28.9 1.7010

1.1025 240 0.2 45.6 44.3 2.8381

1.1293 265 0.2 51.2 50.5 1.4200

Extended delta-bar-delta algorithm:

V [p.u.]L.L.

[km]r [p.u.]

B.S.A.HI[deg.]

B.S.A.EDBD[deg.]

Error [%]

0.9335 125 0.8 75.4 72.9 3.2789

0.9512 155 0.7 42.9 42.1 1.7887

0.9906 175 0.6 56.1 55.7 0.73950.9906 175 0.5 90 88.7 1.4739

1.0502 215 0.4 82.3 84.7 2.9034

1.0595 225 0.3 29.4 29.5 0.4986

1.1025 240 0.2 45.6 46.1 1.1257

1.1293 265 0.2 51.2 52.7 2.8627

Directed random search algorithm:

V [p.u.]L.L.

[km]r [p.u.]

B.S.A.HI[deg.]

B.S.A.DRS[deg.]

Error [%]

0.9335 125 0.8 75.4 76.1 0.9575

0.9512 155 0.7 42.9 44.3 3.2421

0.9906 175 0.6 56.1 56.6 0.8216

0.9906 175 0.5 90 89.6 0.4479

1.0502 215 0.4 82.3 81.1 1.4442

1.0595 225 0.3 29.4 28.7 2.2215

1.1025 240 0.2 45.6 45.3 0.6354

1.1293 265 0.2 51.2 51.9 1.4113

V = voltage at transformer bus before switching, L.L. = line length, r = remanent flux,B.S.AHI = the best switching angle obtained by the harmonic index, B.S.ADBD = the best

switching angle obtained by the DBD, B.S.AEDBD= the best switching angle obtained by the

EDBD, B.S.ADRS= the best switching angle obtained by the DRS, and Error =switching angle

error.


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delta-bar-delta and directed random search algorithms application to reduce transformer switching...

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